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Dçkmrrma` Dçkmrr ma` @xpr`ss @xpr`ss ®

phur QQ Cgb`rtç

2

Uhs r`j`tt`s Dçkmrrma` @xpr`ss d` cm s`kmgl` Jnmjul` d`s r`j`tt`s p`ut ïtr` gltçarç` æ ul k`lu jhkk` prçjgsç `l bms d` pma` d`s ohurlç`s. R`trhuv`z j`s r`j`tt`s `t c`s k`lus d` j` cgvr`t sur c„mppcg c„ mppcg QQ Q Q `t ww.jhk.

4

@spmdhl mu rhuamgc d‗mub`ragl`s

6

Vmkpc`khuss` ahurkmld

2

2

T`rrgl` d` phgsshl `t smuj` jgtrhl

2

Vhtmth` jmi` mu jrmb`

6

Vhïcç` d‗çpglmrds `t phgs jngjn`s

6

Lmvmrgl d` phuc`t

2

Jrhustmd` mux ermkbhgs`s

4

Vht mu e`u d` vhcmgcc` mux trhkp`tt`s

4

Kçcg-kçch d` bcç, theu `t cçauk`s

2

Tmrt` cçaîr` phgr` jhjh

:

Bg`lv`lu` Bg`lv`l u` phur j`tt` d`uxgîk` s`kmgl` d` Dçkmrrma` @xpr`ss Dçjhuvr`z c`s k`lus qu` lhus vhus mvhls jhljhjtçs phur vhus emjgcgt`r j`tt` d`uxgîk` s`kmgl` d` prharmkk`.

Zg vhus l‗utgcgs`z j`s k`lus qu` phur vhus glspgr`r, l‗hubcg`z pms j`s prgljgp`s ? • V`ls`z mux mcgk`lts æ _`rhVhglt™  jhkk` bms` d` vhs r`pms `t jhccmtghls. • R`st`z dmls vhtr` buda`t ZkmrtVhglts® (gc gljcut vhs ZkmrtVhglts n`bdhs). • Ptgcgs`z vhs ZkmrtVhglts jhkk` gc vhus pcmìt , kmgs l` p`rd`z pms d` vu` vhtr` hbo`jtge. • Tçcçjnmra`z c‗mppcg QQ sg vhus l` c‗mv`z pms `ljhr` emgt. J‗`st vhtr` mssgstmlt 24n/24, 1o/1. Bhll` s`kmgl` ! Vcus d‗glehs sur c`s ZkmrtVhglts `t c`s mcgk`lts æ _`rhVhglt™ dmls vhtr` cgvr`t Bg`lv`lu` jn`z QQ hu sur ww.jhk.

C`s p`tgts pcus qug ehlt cm dgstçr`lj` Jnmla`r d‗çtmt d‗`sprgt J`tt` s`kmgl`, `ssmy`z d` kmla`r `l pc`gl jhlsjg`lj`. J`cm sgalg﬍` pr`ldr` shl t`kps, s‗glstmcc`r æ tmbc` smls tçcçvgsghl, prït`r mtt`ltghl mux mcgk`lts qu` vhus kmla`z ? c‗msp`jt d` vhtr` mssg`tt`, c‗hd`ur `t cm t`xtur` d` vhs pcmts. Jhkk`lj`z pmr `ssmy`r æ ul hu d`ux r`pms `t v`l`z pmrtma`r j` qu` j`cm vhus m mpphrtç mv`j vhtr` @qugp` QQ `t c`s mutr`s k`kbr`s dmls vhtr` studgh QQ. Bhua`r ul p`u pcus jnmqu` ohur J`tt` s`kmgl`, `l pcus d`s :666 pms pmr ohur qu` lhus vhus r`jhkkmldhls d` emgr` mu kglgkuk, `ssmy`z d` emgr` c` pc`gl d` EgtVhglts® phur mtt`gldr` vhtr` hbo`jtge kïk` sg vhus l‗mv`z pms b`mujhup d` t`kps. Vhur j`cm, jnhgsgss`z d`s mjtgvgtçs d` ehrj` hu d` jmrdgh jhkk` du vçch d‗mppmrt`k`lt vgt`ss` rmpgd`, d` cm jhurs` sur pcmj`, d`s `x`rjgj`s d` amglma` hu d` kusjucmtghl mv`j j` qu` vhus mv`z shus cm kmgl. R`trhuv`z d`s vgdçhs sur QQ.jhk hlac`t Vrharmkk` `t mrtgjc`s < Bhua`r jhkk` gc k` pcmgt 4

Dçkmrrma` @xpr`ss, rmpp`c du khd` d‗ d‗`kpchg • J`s k`lus shlt bmsçs sur ul buda`t d` 2: ZkmrtVhglts ohurlmcg`rs. J`p`ldmlt, vhus jhlstmt`r`z qu‗gcs vmrg`lt `ltr` 26 `t 20 ZkmrtVhglts pmr ohur, j` qug khltr` jhkk`lt c`s çjhlhkg`s d` j`rtmgl`s ohurlç`s p`uv`lt s` r`phrt`r sur d‗mutr`s. • Cm jhchll` « b`shgl d` pcus ¹ vhus suaaîr` d`s mcgk`lts æ mohut`r hu d`s phrtghls pcus gkphrtmlt`s sg vhtr` buda`t ZkmrtVhglts `st supçrg`ur hu sg vhus shunmgt`z utgcgs`r vhs ZkmrtVhglts n`bdhs. • Uhus phuv`z sugvr` j`s k`lus jhkk` gcs shlt , jnhgsgr pmrkg c`s r`pms d`s dgstçr`lt`s ohurlç`s hu jugsgl`r c`s r`j`tt`s qug vhus shlt prhphsç`s. V`ls`z sgkpc`k`lt æ lht`r hu `lr`agstr`r c`s ZkmrtVhglts d` vhs r`pms æ cm ﬍l d` vhtr`  ohurlç` phur r`st`r dmls vhtr` vhtr` buda`t ZkmrtVhgl ZkmrtVhglts. ts. • L‗nçsgt`z pms æ çjnmla`r c`s mcgk`lts æ _`rhVhglt™ pmr d‗mutr`s jhkk` vhus c` shunmgt`z, s`chl vhs ahùts `t cm smgshl. • C`s bhgsshls l` shlt pms prçjgsç`s  dmls j`s k`lus. Jhlshkk`z =, 0 æ 2 C d` cgqugd` pmr ohur dhlt = C d‗`mu, shgt c‗çqugvmc`lt d` > v`rr`s. D` kïk`, jnhgsgss`z tnç, jmeç hu gleusghl jhkk` vhus c` shunmgt`z kmgs sg vhus mohut`z du cmgt `t du sujr`, jhkpt`z-c`s. @t l‗hubcg`z pms d` jhkpt`r c`s ZkmrtVhglts d` vhs bhgsshls mcjhhcgsç`s, d` vhs shdms `t d` vhs ous d` erugts. • Uhus phuv`z r`kpcmj`r c`s n`rb`s mrhkmtgqu`s, jhldgk`lts `t smuj`s æ 6 ZkmrtVhglts jhkk` vhus c` shunmgt`z, s`chl vhs ahùts. • Uhus phuv`z smc`r `t phgvr`r æ vhtr` jhlv`lmlj`. Ahùt`z thut d` kïk` vhs pcmts mvmlt d` smc`r pugsqu‗gc `st r`jhkkmldç d` cgkgt`r sm jhlshkkmtghl d` s`c. • Vhur c`s r`j`tt`s, vhus dgsphs`z d‗gldgjmtghls ? 2

Lhkbr` d` ZkmrtVhglts pmr p`rshll` / pmrt

 Uçaçtmrg`l  Zmls acut`l  Zmls cmjths` 0

Ohur =

Km ohurlç` æ

V`tgt dço`ul`r

25

2 trmljn`s d` pmgl jhkpc`t (06 a) = jj d` b`urr` = jj d` jhl﬍tur` = ymhurt lmtur` jcmssgqu` = erugt d` smgshl Tnç hu jmeç

Dço`ul`r

+ d` pmgl

6

Mohut`r d`s mkmld`s `﬊cç`s

2

+ = JZ d` cmgt d` jhjh

Wmhurt mu cmgt `ltg`r `t/hu mux erugts

6 = 5 6

+ d` quglhm

6

= erugt d` smgshl = ymhurt lmtur` jcmssgqu`

Dìl`r

4 2 = 6 6 6

7

=26 a d` ﬍c`t d` trugt` jugt `l pmpgccht` mv`j du jgtrhl marçk`ltç mprîs jugsshl d` = JZ d` cmgt d` jhjh, mjjhkpmalç d` =66 a d` phuss`s d‗çpglmrds thkbçs dmls = jj d‗nugc` d‗hcgv` `t d` =16 a d` quglhm jugt = erugt d` smgshl

Jhccmtghl

B`shgl d` pcus 8

1

6 6

Wmhurt mu cmgt `ltg`r `t/hu mux erugts

=6

Bhuddnm bhwc jhkphsç d` =66 a d` c`ltgcc`s v`rt`s jugt`s, d` =06 a d` rgz bcmlj jugt, d` =6 rmdgs `t d‗ul` jmrhtt` `l bâthll`ts mssmgshllç mv`j ul` vglmgar`tt` jhkphsç` d` = jj d‗nugc` `t d` = jj d` vglmgar` = pht (=66 a) d` emgss`cc`

6 0 6

+ d` rgz

= 6 4

+ = jj d‗nugc`

Uhus phuv`z r`kpcmj`r c` egc`t d` trugt`, c` cmgt d` jhjh, c`s phuss`s d‗çpglmrds, `t c‗nugc` 4 du dìl`r pmr cm r`j`tt` d‗`spmdhl d‗`spmdhl mu rhuamgc, pma` jg-jhltr`.

5

@spmdhl mu rhuamgc d‗mub`ragl`s Vrçpmrmtghl =0 kgl | Jugsshl 27 kgl | Vhur 4 p`rshll`s

4 = mub`ragl` (:66 a) 2 thkmt`s bg`l kùr`s (466 a) = hgalhl bcmlj (=66 a) = ahuss` d‗mgc = jgtrhl omul` 4 jj d‗nugc` d‗hcgv` =/2 jj d‗hrgaml 4 trmljn`s d‗`spmdhl d‗`spmdhl (4>6 a) 2 jj d` p`rsgc nmjnç Z`c, phgvr`

Vhurquhg pms 8 R`kpcmj`z c` phgsshl s`chl vhtr` ahùt, pmr du jmbgccmud pmr `x`kpc`.

= Rglj`r `t jhup`r c‗mub`ragl` `l 2. C`s `lv`chpp`r dmls

du egck `t c`s k`ttr` mu kgjrh-hld`s. Jugr` 0 kgl (>66 Q). Cmgss`r Cmgss `r tgçdgr. 2 V`c`r `t jhup`r c`s thkmt`s `l dçs. V`c`r `t nmjn`r

c‗hgalhl pugs c‗mgc. Vr`ss`r =/2 jgtrhl, jhup`r c‗mutr` =/2 `l 4 rhld`cc`s. Rçjupçr`r cm pucp` d`s mub`ragl`s. : Jnmuee`r 2 jj d‗nugc` dmls ul` jmss`rhc`. W emgr` su`r

c‗hgalhl = kgl, æ e`u dhux. Mohut`r c‗mgc `t cm pucp` d‗mub`ragl`, r`ku`r = kgl. Gljhrphr`r c`s dçs d` thkmt`s mv`j c`ur ous. Zmc`r, phgvr`r `t pmrs`k`r d‗hrgaml. Jhuvrgr `t cmgss`r jugr` =6 kgl, æ e`u dhux, pugs 0 kgl æ dçjhuv`rt, `l r`kumlt. 4 Mssmgshll`r c‗`spmdhl. Jnmuee`r c` r`stmlt d‗nugc` dmls

ul` smut`us` `t y emgr` r`v`lgr c‗`spmdhl : kgl d` jnmqu` jôtç æ e`u vge pugs khy`l. Mu d`rlg`r khk`lt mrrhs`r d` ous d` jgtrhl `t smuphudr`r d` p`rsgc nmjnç. 1

Ohur 2

Km ohurlç` æ

V`tgt dço`ul`r

2:

06 a d` flhjhls flhjhl s d‗mvhgl` = erhkma` erhkm a` bcmlj 6 % lmtur` = erugt d` smgshl Tnç hu jmeç

Dço`ul`r

+ d` flhjhls d‗mvhgl` d‗mvhgl` Erhkma` bcmlj æ 26 %

6 = 6

+ d` dgld`

6 6

Mohut`r du ﬍c`t d` bmjhl R`kpcmj`r cm thkmt` pmr d` cm smuj` thkmt` jugsglç`

4

2

= smcmd` d` erugt d` smgshl = bgsjugt s`j

Dìl`r

0 = 6 6

0

=66 a d` jnhu rhua`, mssmgshllç mv`j = jj d‗nugc` `t = jj d` vglmgar` =26 a d` jub`s d` bcmlj d` dgld` jugts æ cm phïc` sur ul` e`ugcc` d` jugsshl, pugs kgohtçs =0 kgl mv`j 266 a d` nmrgjhts bcmljs, =66 a d` pucp` d` thkmt` `t d` c‗hrgaml = pht (=66a) d` emgss`cc`

Jhccmtghl

B`shgl d` pcus 8

5

6 2

=6

=26 a d` pmvç d` smukhl jugt 6 mu ehur, ehur, mjjhkpmalç mjjhkpma lç d` =06 a d` phc`ltm jugt` lmtur` : `t d` =06 a d` oucg`ll` d` cçauk`s 6 r`v`lu` æ cm phïc` dmls = jj d‗nugc` = :6 a d` aruyîr` mjjhkpmalç d` 4 2 20 a d` bmau`tt` 6 = erugt d` smgshl

+ d` phc`ltm Mohut`r du pmrk`sml `t d`s thkmt`s sçjnç`s + d` bmau`tt`

Uhus phuv`z r`kpcmj`r c` phuc`t `t c`s nmrgjhts bcmljs æ cm thkmt` 6  du dço`ul`r pmr cm r`j`tt` du lmvmrgl lmvmrgl d` phuc`t d` cm pma` 2= `t c` pmvç d` smukhl 2  du dìl`r pmr cm r`j`tt` d` t`rrgl` d` phgsshl `t smuj` jgtrhl, pma` jg-jhltr`.

>

T`rrgl` d` phgsshl `t smuj` jgtrhl Vrçpmrmtghl 20 kgl | Jugsshl 47 kgl | R`phs : n | Vhur 5 p`rshll`s

2 066 a d` ﬍c`ts d` k`rcml =66 kc d` vgl bcmlj s`j =6 hgalhls ar`chts sura`cçs =66 a d` jr`v`tt`s rhs`s dçjhrtgquç`s 266 a d` lhgx d` pçthljc` mv`j jhrmgc 46 a d` ymhurt brmss ç 6 % lmtur` = jj d` jhlj`ltrç d` thkmt`s : Śues

= Vrçjnmuee`r c` ehur æ =>6 ¶J (tn. 5). Vhrt`r æ çbuccgtghl c`

vgl bcmlj `t c`s hgalhls çkgljçs pugs v`rs`r sur d`s jub`s d` phgsshl, kçcmla`r `t rçs`rv`r mu ermgs. Jhup`r c`s jr`v`tt`s, dçtmjn`r c` jhrmgc d`s pçthljc`s `t c`s kgx`r mv`j c` ymhurt `t c` jhlj`ltrç d` thkmt`s. 2 Çahutt`r c` phgsshl `t c` kgx`r `l mohutmlt c`s bcmljs

d‗Śues. Zmc`r `t phgvr`r phgv r`r.. U`rs`r =/2 d` cm prçpmrmtghl dmls ul` t`rrgl` `t cgss`r. Çtmc`r cm khuss` d` jr`v`tt`s, dçphs`r c`s pçthljc`s `t r`jhuvrgr du r`st` d` prçpmrmtghl. Jhuvrgr d‗ul` e`ugcc` d‗mcukglguk trhuç`. @lehurl`r mu bmgl-kmrg` 40 kgl. Tgçdgr, r`tgr`r c` ous `t rçs`rv`r mu ermgs.

266 a d` cmgt d`kg-çjrçkç jhlj`ltrç lhl sujrç

: Bmttr` c`s omul`s d‗Śues mv`j =66 a d` cmgt `t jnmuee`r = kgl

2 jj d` eçjuc` d` phkk`s d` t`rr`

æ e`u khy`l `l ehu`ttmlt. Mohut`r cm eçjuc` dçcmyç` mv`j =66 a d` cmgt thut `l jhltglumlt d` ehu`tt`r = æ 2 kgl.

= jj d` b`urr` dhux C` ous d` : jgtrhls (56 kc) Z`c, phgvr` bcmlj

4 Nhrs du e`u, mohut`r c` b`urr` `t c` ous d` jgtrhl. Rçs`rv`r

mu ermgs. Z`rvgr cm t`rrgl` `l trmljn`s, mv`j d` cm smuj`. 7

Ohur :

Km ohurlç` æ

V`tgt dço`ul`r

26

2 trmljn`s d` pmgl jhkpc`t (06 a) = jj d` b`urr` = jj d` jhl﬍tur` = ymhurt lmtur` jcmssgqu` = erugt d` smgshl Tnç hu jmeç

Dço`ul`r

+ d` pmgl

:

+ d` bmv`tt` d` bŚue 

6 =

Mohut`r du pmrk`sml

Wmhurt mu cmgt `ltg`r `t/hu mux erugts

Mohut`r d`s eçjuc`lts 6 6 2

=

= erhkma` bcmlj 6 % lmtur`

Dìl`r

4 2 = 6 6 6

5

=26 a d` bmv`tt` d` bŚue argccç`, mjjhkpmalç` d` 266 a d` jub`s d‗mub`ragl` r`v`lus dmls = jj nugc` d‗hcgv` mv`j d`s e`ugcc`s bmsgcgj `t d`s eîv`s jugt`s Jhkpht` d` phkk` smls sujr`s mohutçs, r`jhuv`rt` r`jhuv`rt` d‗= d‗ = bgsjugt s`j çkg`ttç `l jrukbc`

Jhccmtghl

B`shgl d` pcus 8

1

=

Erhkma` bcmlj æ 26 %

5

=66 a d` theu kmrglç mv`j = JZ d` smuj` shom smcç`, mjjhkpmalç d` =06 a d` bhucahur jugt `t d` =06 a d` phtgrhl rôtg mu ehur mv`j = jj d‗nugc` d‗hcgv` `t du tnyk = erhkma` erhkm a` bcmlj 6 % lmtur` = jj d` kg`c = erugt d` smgshl

6 6 : 6 = = = 6

+ d` bhucahur Mohut`r d`s rmgsgls s`js `t d`s lhgx d` jmohu Erhkma` bcmlj æ 26 %

Uhus phuv`z r`kpcmj`r cm jhkpht` `t c` c ` bgsjugt 2 du dìl`r pmr cm r`j`tt` d` jrhustmd` mux ermkbhgs`s, pma` jg-jhltr` jg-jh ltr` `t c` theu kmrglç, c` bhucahur `t c` phtgrhl 4 du dìl`r pmr cm r`j`tt` d` kçcg-kçch d` bcç, theu `t cçauk`s d` cm pma` 22.

=6

Jrhustmd` mux ermkbhgs`s Vrçpmrmtghl =0 kgl | Jugsshl =0 kgl | Vhur 4 p`rshll`s

2 2 Śues = JZ d` phudr` d‗mkmld`s = smjn`t d` sujr` vmlgccç 2 jj d‗`mu d` rhs` 4 e`ugcc`s d` brgji =06 a d` ermkbhgs`s

= Vrçjnmuee`r c` ehur æ =>6 ¶J (tn. 5). Bmttr` c`s Śues mv`j cm

phudr` d‗mkmld`s, c` sujr` vmlgccç `t c‗`mu d` rhs`. 2 Çtmc`r c`s e`ugcc`s d` brgji sur c` pcml d` trmvmgc. C`s pcg`r

`l 2. C`s `lehlj`r dmls d`s khuc`s æ kueegls ec`xgbc`s d` 5 jk d` dgmkîtr` `lvgrhl. W v`rs`r cm prçpmrmtghl mux mkmld`s `t y `lehlj`r c`s ermkbhgs`s `ltgîr`s. : @lehurl`r =2 æ =0 kgl, ousqu‗æ j` qu` c`s e`ugcc`s d` brgji

shg`lt dhrç`s. Dçaust`r tgîd` hu erhgd. Vhurquhg pms 8 R`trhuv`z j`tt` r`j`tt` `t pcus `ljhr` dmls c` Jheer`t Cgb`rtç.

==

Ohur 4

Km ohurlç` æ

V`tgt dço`ul`r

25

06 a d` flhjhls flhjhl s d‗mvhgl` = erhkma` erhkm a` bcmlj 6 % lmtur` = erugt d` smgshl Tnç hu jmeç

Dço`ul`r

0 = 6 6

+ d` flhjhls d‗mvhgl` d‗mvhgl` Erhkma` bcmlj æ 26 %

6 = 1

= Śue d` pcus

=6

2 Śues mu pcmt, jugts mv`j = jj d‗nugc` dmls ul` phïc`, mjjhkpmalçs d` 266 a d` pât`s jugt`s typ` emremcc` `t d` =06 a d` brhjhcgs, marçk`ltçs d` : JZ d` smuj` thkmt` jugsglç` = ymhurt lmtur` jcmssgqu` mv`j = jj jhl﬍tur` = erugt d` smgshl

Jhccmtghl

6 = 6 = 6

+ d` pât`s Mohut`r d`s mccuk`tt`s d` bmjhl Mohut`r du aruyîr` râpç Wmhurt mu cmgt `ltg`r `t/hu mux erugts

2

= trmljn` (26 a) d` pmgl brghjnç

Dìl`r

B`shgl d` pcus 8

5

2

+ = trmljn` d` pmgl brghjnç Mjjhkpmal`r d‗ul jmppujjglh

>

Kçcmla` d` =66 a d` phgvrhls 06 a d` kmès `t : thkmt`s sçjnç`s, mssmgshllç mv`j = jj d‗nugc` d‗hcgv` `t = jj d` vglmgar` Egc`t d` k`rcml jugt mu ehur, mjjhkpmalç d` bcmljs d` phgr`mux jugts æ cm vmp`ur trîs ehldmlts, pugs marçk`ltç d` = JZ d` jrîk` ermìjn` mccçaç` m ccçaç` =0 % :6 a erhkma` d` jnîvr` ermgs mjjhkpmalç d` 20 a d` bmau`tt` = erugt d` smgshl

6 6 = = 6 6

Mohut`r d`s eçjuc`lts + d` k`rcml

6 = : 2 6

+ = JZ J Z d` jrîk` æ =0 % Jhktç + d` bmau`tt`

Uhus phuv`z r`kpcmj`r c` egc`t d` k`rcml, c`s bcmljs bcmlj s d` phgr`mux `t cm jrîk` 6 du dìl`r pmr cm r`j`tt` d` pmkpc`khuss` ahurkmld, pma` jg-jhltr`.

=2

Vmkpc`khuss` ahurkmld Vrçpmrmtghl 26 kgl | Jugsshl 0 kgl | Vhur 4 p`rshll`s

6 4 Śues `ltg`rs 2 p`tgts pmkpc`khuss`s rhs`s =26 a d` jr`v`tt`s rhs`s jugt`s `t dçjhrtgquç`s =:6 a d` kmjçdhgl` d` cçauk`s `l bhìt` = hgalhl bcmlj mv`j tga`s v`rt`s = ymhurt brmssç 6 % lmtur` = pgljç` d` pmprgim Z`c, phgvr`

Vhurquhg pms 8 R`kpcmj`z c`s jr`v`tt`s pmr d`s kg`tt`s d` jrmb`.

= Dçphs`r c`s Śues dmls ul` jmss`rhc` d‗`mu erhgd`.

Jhuvrgr `t phrt`r æ çbuccgtghl 0 kgl. Cmgss`r r`phs`r =6 kgl nhrs du e`u `t dmls c‗`mu. Jhup`r c`s pmkpc`khuss`s `l d`ux. Dçtmjn`r c`s qumrtg`rs, c`s jhup`r `l khrj`mux `t `lc`v`r c`s k`kbrml`s bcmljn`s. Dçtmgcc`r c`s jr`v`tt`s `l dçs, çahutt`r cm kmjçdhgl` d` cçauk`s. V`c`r `t nmjn`r c‗hgalhl. Jgs`c`r cm bms` d`s tga`s. K`ttr` thus c`s glarçdg`lts mu eur `t æ k`sur` dmls ul p`tgt smcmdg`r. 2 Çjmc`r c`s Śues shus c‗`mu erhgd`. Jhup`r c`s bcmljs `l

egl`s cmlgîr`s, c`s mohut`r mu kçcmla` `t pcmj`r mu ermgs. Dmls ul bhc, çjrms`r c`s omul`s æ cm ehurjn`tt` pugs c`s kçcmla`r mv`j c` ymhurt `t ul` pgljç` d` pmprgim. Zmc`r, phgvr`r `t rçs`rv`r mu ermgs = n. Mu khk`lt d` s`rvgr, mohut`r cm smuj` mu ymhurt mu kçcmla`. Z`rvgr dmls d`s mssg`tt`s d` s`rvgj`, d`s p`tgts bhcs hu c`s =/2 pmkpc`khuss`s çvgdçs. =:

Ohur 0

Km ohurlç` æ

V`tgt dço`ul`r

24

2 trmljn`s d` pmgl jhkpc`t (06 a) = jj d` b`urr` = jj d` jhl﬍tur` = ymhurt lmtur` jcmssgqu` = erugt d` smgshl Tnç hu jmeç

Dço`ul`r

+ d` pmgl

2 6 6 2 4

+ d` s`khuc`

Wmhurt mu cmgt `ltg`r `t/hu mux erugts

= 6 6

2

= erugt d` smgshl = bgsjugt s`j

Dìl`r

4 2 = 6 6 6

7

Zmcmd` jhkphsç` d` >6 a d` s`khuc` jugt`, =66 a d` kg`tt`s d` jrmb` `t smcmd` v`rt`, =6 a lhgx sîjn`s `t d` :6 a d` jub`s d` jhktç mssmgshllç` mv`j = jj d` vglmgar`tt` kçcmlaç` æ = jj d‗`m d ‗`muu = erugt d` smgshl

Jhccmtghl

B`shgl d` pcus 8

1

6 2

5

=26 a d` ﬍c`t kgalhl d` phrj jugt mu ehur, mjjhkpmalç d` =06 a d` c`ltgcc`s jhrmgc jugt`s =06 a d` jnhu-fl`ur jugt, mv`j = jj d‗nugc` d‗hcgv`, Jhrgmldr` `t jurry = erhkma` erhkm a` bcmlj 6 % lmtur` = jj d` kg`c

: 6 6 = 6 = =

+ d` ﬍c`t kgalhl Mohut`r d`s prul`mux + d` c`ltgcc`s

Erhkma` bcmlj æ 26 % lmtur`

Uhus phuv`z r`kpcmj`r cm s`khuc` `t c`s kg`tt`s d` jrmb` 2 du dìl`r pmr cm r`j`tt` d` phtmth` jmi` mu jrmb` `t mux n`rb`s ermgjn`s, pma` jg-jhltr`.

=4

Vhtmth` jmi` mu jrmb` Vrçpmrmtghl 26 kgl | Jugsshl 46 kgl | Vhur > pmc`ts

2 066 a d` phkk`s d` t`rr` = bhuqu`t d‗n`rb`s ermìjn`s ? ﬍l`s n`rb`s, jhrgmldr`, ml`tn = Śue  466 a d` kg`tt`s d` jrmb` = JZ d` emrgl` = jj d‗nugc` d‗hcgv` ]u`cqu`s e`ugcc`s d` kâjn` 2 jgtrhls omul`s Z`c, phgvr`

= Çpcujn`r c`s phkk`s d` t`rr` `t c`s jhup`r `l arhs

khrj`mux. C`s pchla`r dmls ul` jmss`rhc` d‗`mu bhugccmlt` smcç`. Çahutt`r, v`rs`r c` thut dmls ul smcmdg`r `t cmgss`r r`erhgdgr. Çjrms`r `l purç` æ c‗mgd` d‗ul pr`ss`-purç` kmlu`c. 2 Jgs`c`r c`s n`rb`s mu-d`ssus, mohut`r c‗Śue `t kçcmla`r æ

cm jugccîr` `l bhgs. Gljhrphr`r c`s kg`tt`s d` jrmb` `t kçcmla`r d` lhuv`mu. lhuv` mu. Zmc`r, Zmc`r, phgvr`r. Ehrk`r > pmc`ts, c`s c` s pmss`r dmls ul p`u d` emrgl`. : Emgr` jnmuee`r ul` phïc` mltgmdnçsgv` mv`j c‗nugc` d‗hcgv`.

Dçphs`r c`s pmc`ts `t cmgss`r dhr`r : æ 4 kgl d` jnmqu` jôtç. Z`rvgr bg`l jnmud mv`j d` cm kâjn` `t d`s qumrtg`rs d` jgtrhl.

Vhurquhg pms 8 Vhur pcus d` ahurkmldgs`, rçmcgs`r ul` kmyhllmgs` `l çkucsgegmlt = Śue, = JZ d` khutmrd`, 2 JZ d` ymhurt ymhur t jcmssgqu` `t 2 JZ d‗nugc` d‗hcgv`. Pl` ehgs khltç`, mohut`r = J Z d` jâpr`. = ulgtç ZkmrtVhglts/ Zkmr tVhglts/p`rshll` p`rshll`

=0

Ohur 5

Km ohurlç` æ

V`tgt dço`ul`r

2:

06 a d` flhjhls flhjhl s d‗mvhgl` = erhkma` erhkm a` bcmlj 6 % lmtur` = erugt d` smgshl Tnç hu jmeç

Dço`ul`r

+ d` flhjhls d‗mvhgl` d‗mvhgl` Erhkma` bcmlj æ 26 %

6 = 6 6 2 2 6 6 =

+ d` phkk`s d` t`rr`

Wmhurt mu cmgt `ltg`r `t/hu mux erugts

6

= smcmd` d` erugt d` smgshl

Dìl`r

0 = 6 6

5

=66 a d` jrudgtçs mssmgshllç`s mv`j = jj d` vglmgar`tt` kçcmlaç` æ = jj d‗`m d ‗`muu =26 a d‗mgaugcc`tt`s d` phuc`t argccç`s, =66 a d‗çjrmsç d` phkk`s d` t`rr` mv`j = jj d` b`urr` =06 a d` nmrgjhts v`rts = ymhurt lmtur` jcmssgqu` = jj d` jhl﬍tur`

Jhccmtghl

B`shgl d` pcus 8

5

6

==

=26 a d‗`sjmchp` d` v`mu argccç` mjjhkpmalç` d` =06 a d` pmtmt` dhuj` `t d` =06 a d` jnmkpgalhls smutçs dmls = jj d‗nugc` æ cm phïc` = ymhurt lmtur` jcmssgqu` mv`j 2 jj d` jhl﬍tur`

2

+ d‗`sjmchp` d` v`mu

5 6 = 6 2

+ d` pmtmt` dhuj`

Wmhurt mu cmgt `ltg`r `t/hu mux erugts

Uhus phuv`z r`kpcmj`r c` phuc`t, c`s phkk`s d` t`rr` `t c`s nmrgjhts du dço`ul`r 4 pmr cm r`j`tt` d` pht mu e`u d` vhcmgcc` vhcmgcc` mux trhkp`tt`s d` cm khrt d` cm pma` 2:, `t c` ymhurt lmtur` `t cm jhlegtur` 2 du dìl`r pmr cm r`j`tt` d` tmrt` cçaîr` phgr` jhjh, pma` jg-jhltr`.

=5

Tmrt` cçaîr` phgr` jhjh Vrçpmrmtghl =6 kgl | Jugsshl 26 kgl | Vhur 4 p`rshll`s

2 : phgr`s :66 a d` erhkma` bcmlj lmtur` 6 % 2 Śues =/2 jgtrhl 2 jj d` lhgx d` jhjh râpç`, sîjn` 2 jj d` sujr` `l phudr` : e`ugcc`s d` k`ltn`

= Vrçjnmuee`r c` ehur æ 2=6 ¶J (tn. 1). Çpcujn`r `t jhup`r

c`s phgr`s `l egl`s cmk`cc`s. C`s dgsphs`r, `l c`s cmgssmlt s` jn`vmujn`r, dmls ul khuc` d` => jk d` dgmkîtr`, r`jhuv`rt d‗ul` e`ugcc` d` jugsshl. 2 Ehu`tt`r c` erhkma` bcmlj mv`j c`s Śues, mohut`r c` z`st`

râpç du jgtrhl `t cm lhgx d` jhjh. U`rs`r c` thut sur c`s phgr`s, smuphudr`r d` sujr` `t `lehurl`r 26 kgl. Cmgss`r r`erhgdgr,, dçkhuc`r `t dçjhr`r d` e`ugcc`s d` k`ltn`. r`erhgdgr

=1

Ohur 1

Km ohurlç` æ

V`tgt dço`ul`r

=7

= trmljn` d` pmgl jhkpc`t (20 a) = Śue dur jhupç `l 2 = trmljn` d` omkbhl bcmlj = erhkma` ehldu = erugt d` smgshl Tnç hu jmeç

Dço`ul`r

2 6 2 2 6 6

+ d` pmgl + d` omkbhl + d` erhkma`

7

Jngcg jhl jmrl` jugsglç mv`j =66 a d` st`mi s t`mi nmjnç 0 % jugt æ cm phïc` mv`j = jj d‗nugc` pugs kgohtç =0 kgl mv`j d`s nmrgjhts rhua`s jugts, d`s phgvrhls rhua`s `l cmk`cc`s `t du pmprgim = erhkma` erhkm a` bcmlj 6 % lmtur` marçk`ltç d` =0 a mkmld`s `t d` = JZ jhucgs d` erugt

Jhccmtghl

+ d` st`mi : = 6 6 6 = : =

Mohut`r du rgz

Erhkma` bcmlj æ 26 %

6

= erugt d` smgshl

Dìl`r

B`shgl d` pcus 8

5

6

4

U`chutç prçpmrç mv`j 266 a d` phgs jmssçs `t 2 pmlmgs jugts æ c‗`mu pugs kgxçs mv`j = JZ d` jrîk` ermgjn` mccçaç` m ccçaç` =0 % `t = pgljç` d` jukgl surkhltç d` =66 a d` jub`s d` theu e`rk` argccçs smuphudrç d` 2 JZ d` pmrk`sml râpç = erugt d` smgshl

6 6 = 6 6 : 6

Mohut`r d`s armgl`s d` sçsmk`

Mohut`r ul eçjuc`lt

+ d` pmrk`sml

Uhus phuv`z r`kpcmj`r c` v`chutç `t c` theu 6 d‗çpglmrds `t phgs jngjn`s, pma` jg-jhltr`.

=>

du dìl`r pmr pmr cm r`j`tt` d` phïcç`

Vhïcç` d‗çpglmrds `t phgs jngjn`s Vrçpmrmtghl =5 kgl | Jugsshl 26 kgl | Vhur 5 p`rshll`s

6 2 hgalhls 2 ahuss`s d‗mgc = jj d` agla`kbr` ermgs 2 jj d‗nugc` d‗hcgv` 2 jj d` jukgl 406 a d` thkmt`s jhljmssç`s mu lmtur`c :66 a d` phgs jngjn`s jugts :66 a d‗çpglmrds ermgs 2 JZ d‗`mu = JZ d` ous d` jgtrhl

= Çpcujn`r `t nmjn`r sçpmrçk`lt c`s hgalhls, c‗mgc `t c`

agla`kbr`. Emgr` jnmuee`r c‗nugc` dmls ul` jmss`rhc` æ e`u dhux. Mohut`r c`s hgalhls `t ul` d`kg jugccîr` æ jmeç d` s`c. Jugr` =6 kgl `l r`kumlt erçqu`kk`lt. Mohut`r c‗mgc, c` jukgl `t c` agla`kbr`. Emgr` r`v`lgr = kgl. Mohut`r c`s thkmt`s jhljmssç`s `t c`s phgs jngjn`s. Bg`l kçcmla`r. 2 Mohut`r `lsugt` c`s çpglmrds `t c‗`mu. Bg`l kçcmla`r `t

jugr` æ jhuv`rt 0 æ =6 kgl ousqu‗æ j` qu` c`s çpglmrds thkb`lt. Mohut`r c` ous d` jgtrhl, cm jhrgmldr` jgs`cç` `t c` s`c. Z`rvgr d` sugt`.

=6 a d` jhrgmldr` ermìjn` Z`c

=7

Lmvmrgl d` phuc`t Vrçpmrmtghl 20 kgl | Jugsshl :6 kgl | Vhur 4 p`rshll`s

6 =20 a d` jmrhtt`s =20 a d` lmv`ts =20 a d` nmrgjhts v`rts =66 a d‗hgalhls lhuv`mux 066 a d` bcmljs d` phuc`t =20 a d` nmrgjhts bcmljs `l bhìt` : JZ d` jhlj`ltrç d` thkmt`s 2 JZ rms` d` p`rsgc jgs`cç = pgljç` d` pgk`lt `l phudr` Z`c, phgvr` du khucgl

= Vrçpmr`r c`s cçauk`s `t c` phuc`t `l jub`s. Çahutt`r c`s

nmrgjhts bcmljs `t rçjupçr`r c` ous. C` kçcmla`r mv`j c` jhlj`ltrç d` thkmt`s `t : JZ d‗`mu, smc`r `t phgvr`r. Dgsphs`r jmrhtt`s `t lmv`ts dmls ul rçjgpg`lt, mohut`r =/: d` cm smuj`, bg`l kçcmla`r. 2 Vcmj`r c` phuc`t dmls ul mutr` rçjgpg`lt mv`j c`s hgalhls `t

c`s nmrgjhts bcmljs, gljhrphr`r =/: d` cm smuj`, kçcmla`r. Cmgss`r kmrgl`r j`s 2 kçcmla`s mu ermgs = n, `l r`kumlt. : Emgr` bhugccgr d` c‗`mu smcç` pugs y pchla`r c`s nmrgjhts

v`rts, `t jugr` > kgl. Çahutt`r `t rçs`rv`r. Emgr` jnmuee`r d` c‗`mu dmls cm pmrtg` bmss` du jugt vmp`ur. Jugr` c`s jmrhtt`s `t c`s lmv`ts æ cm vmp`ur =6 kgl. Mohut`r c` phuc`t `t c`s hgalhls, kçcmla`r `t jugr` =6 kgl. Gljhrphr`r c`s nmrgjhts v`rts `t c` r`stmlt d` smuj` : kgl. 4 U`rs`r dmls ul` jhjhtt` `t jugr` æ e`u trîs dhux 0 kgl.

Z`rvgr jnmud, pmrs`kç d` p`rsgc jgs`cç `t d‗ul` phglt` d` pgk`lt. 26

Kçcg-kçch d` bcç, theu `t cçauk`s Vrçpmrmtghl 0 kgl | Jugsshl =2 kgl | Vhur 4 p`rshll`s

4 =20 a d` p`rc`s d` bcç jru`s `l smjn`t 266 a d` theu e`rk` 2 jj d‗nugc`s d‗hcgv` 2 JZ d‗hgalhl jhupç sura`cç = pgljç` d` jhrgmldr` `l phudr` 266 a d` brulhgs` d` cçauk`s kçdgt`rrmlç`ls mu lmtur`c sura`cç` 2 JZ d` jgbhuc`tt` sura`cç` Z`c, phgvr`

= Vhrt`r =,0 C d‗`mu smcç` æ çbuccgtghl, pchla`r c` smjn`t d`

p`rc`s d` bcç `t jugr` 0 kgl æ p`tgts erçkgss`k`lts. R`tgr`r `t çar`l`r dmls ul rçjgpg`lt. V`ldmlt j` t`kps, çahutt`r c` theu `t c` jhup`r `l p`tgts dçs d` = jk. 2 Emgr` jnmuee`r c‗nugc` dmls ul` smut`us` mltgmdnçsgv`, y

emgr` r`v`lgr c`s hgalhls `t c`s dçs d` theu 2 kgl, æ e`u khy`l. Zmc`r, phgvr`r `t smuphudr`r d` jhrgmldr` `l phudr`. Mohut`r cm brulhgs` d` cçauk`s `t phursugvr` cm jugsshl 4 kgl thut `l r`kumlt. Zmc`r `t phgvr`r. Gljhrphr`r c` bcç `t cm jgbhuc`tt`, kçcmla`r = kgl æ e`u dhux. R`jtgeg`r c‗ c ‗mssmgshll`k`lt sg lçj`ssmgr`.

Vhurquhg pms 8 R`trhuv`z j`tt` r`j`tt` `t pcus `ljhr` dmls c` cgvr` C`s @ss`ltg`cc`s.

2=

Vht mu e`u d` vhcmgcc` mux trhkp`tt`s Vrçpmrmtghl :6 kgl | Jugsshl = n | Vhur 4 p`rshll`s

4 46a d` trhkp`tt`s d` cm khrt sîjn`s = jugss` d` phuc`t smls cm p`mu 2 jmrhtt`s khy`ll`s 4 p`tgt`s brmljn`s d` jçc`rg = hgalhl rhua` 4 p`tgts lmv`ts 4>6 a d` phkk`s d` t`rr` BE=0 4 ﬍c`ts d` phuc`t =4 a d` eçjuc` d` phkk` d` t`rr` J`re`ugc Z`c, phgvr`

= Rçnydrm Rçnydrmt`r t`r c`s trhkp`tt`s = n dmls c‗ c ‗`mu erhgd`. Jhup`r cm

jugss` `l >, `t jugr` dmls = C d‗`mu erçkgssmlt` :6 kgl. 2 Vrçpmr`r c`s cçauk`s `t jugr` dmls : C d‗`mu bhugccmlt`

smcç`. Jugr` c`s phkk`s d` t`rr` æ pmrt, dçpmrt `mu erhgd`. Mohut`r :66 kc d‗`mu d‗`mu d` jugsshl d`s cçauk`s dmls j`cc` d` cm jugss` phur rçmcgs`r c` bhugcchl d` pht-mu-e`u. : Rhuc`r c`s egc`ts d` phuc`t dmls du egck pugs c`s pcmj`r dmls

c‗`mu erçkgssmlt` d`s cçauk`s, mohut`r c`s jnmkpgalhls `t jugr` 0 kgl. Rçs`rv`r 26 kgl. 4 V`ldmlt j` t`kps, phrt`r æ çbuccgtghl c` bhugcchl d`

pht-mu-e`u. Rçdugr` d` khgtgç, ôt`r cm jugss` `t egctr`r. Vrçc`v`r ul` chujn` chujn` `t y dçcmy`r cm eçjuc`, cm k`ttr` dmls c` bhugcchl `t ehu`tt`r phur çpmgssgr. Mssmgshll`r. 0 Dçegck`r c` phuc`t `t lmpp`r d` smuj` s muj` bcmljn`. Emgr`

bhugccgr c` r`st` d` bhugcchl mv`j c`s jnmkpgalhls. Kgx`r. Dr`ss`r `t pmrs`k`r d` pcujn`s d` j`re`ugc ermgs. 22

Cgst` d` jhurs`s Mu rmyhl prgk`ur

Mu rmyhl çpgj`rg`

Mu rmyhl vgmld` `t vhcmgcc`

Mub`ragl`s Bcmljs d` phgr`mux Brhjhcgs Jmrhtt`s Jnmkpgalhls Jnhu-fl`ur Jnhu rhua` Jgtrhl Jrudgtçs Eîv`s Erugts d` smgshl Nmrgjhts v`rts Oucg`ll` d` cçauk`s Vmlmgs Vmtmt`s dhuj`s Vhgvrhls Vhkk`s d` t`rr` Vhtgrhl Vhuss`s d‗çpglmrds Rmdgs Zmcmd` v`rt`

Mkmld`s `t Lhgx Bmau`tt`, Vmgl jhkpc`t `t Vmgl brghjnç Bgsjugt s`j Bhucahur Jmeç / Tnç Jhl﬍tur`, Kg`c `t Jhucgs d` erugts Echjhls d‗mv d‗mvhgl` hgl` Nmrgjhts rhua`s `t bcmljs Nugc` Cmgt d` jhjh C`ltgcc`s v`rt`s `t jhrmgc Kmès `t Vhgs jmssçs Vât`s typ` emremcc`, ]uglhm `t Rgz Vhc`ltm Vucp` d` thkmt` Zmuj` shom smcç` Zmuj` thkmt` jugsglç` Z`khuc` Thkmt`s sçjnç`s sçj nç`s Uglmgar`

Mgaugcc`tt`s d` phuc`t Bmv`tt` d` bŚue  Bcmlj d` dgld` @sjmchp` d` v`mu Egc`t kgalhl d` phrj Omkbhl bcmlj Zt`mi nmjnç 0 %

Mu rmyhl ermgs

Mu rmyhl phgsshl

Egc`t d` k`rcml Egc`t d` trugt` Kg`tt`s d` jrmb` Vmvç d` smukhl Mu rmyhl çpgj`s `t jhldgk`lts

Bmsgcgj Jhrgmldr` Jukgl Jurry Hrgaml Vmprgim Tnyk

B`urr` Jhkpht` smls sujr`s mohutçs Jhktç Jrîk` ermgjn` mccçaç` =0% Emgss`cc` Erhkma` bcmlj 6% lmtur` Erhkma` d` jnîvr` ermgs Erhkma` ehldu Aruyîr` Œues Vmrk`sml râpç Theu Wmhurt Wm hurt lmtur` jcmssgqu` jcms sgqu`

2:

C` systîk` d` p`rt` d` phgds ZkmrtVhglts ZkmrtVhglts `t c`s dhjuk`lts du prharmkk` shlt cm prhprgçtç d` QQ Glt`rlmtghlmc, Glj. `t rçs`rvçs æ c‗utgcgsmtghl `xjcusgv` d`s k`kbr`s d` QQ phur p`rdr` `t kmglt`lgr c`ur phgds. Thut mutr` usma`, r`prhdujtghl hu dgstrgbutghl `st strgjt`k`lt glt`rdgt. L@ V@PT ÏTR@ U@LDP. C` chah pmstgcc` QQ, QQ, ZkmrtVhglts `t VHGLTZ shlt d`s kmrqu`s dçphsç`s d` QQ Glt`rlmtghlmc, Glj. QQ Cgb`rtç `st cm kmrqu` d` QQ Glt`rlmtghlmc, Glj. C‗mppcg QQ `t c`s hutgcs dgagtmux shlt rçs`rvçs mux k`kbr`s mymlt shusjrgt ul mbhll`k`lt. 26=447 ©26=> QQ Glt`rlmtghlmc, Glj. Thus drhgts rçs`rvçs. Gkprgkç `l B`cagqu`.

C` bg`l-ïtr` qug vhus rçussgt.